Supergeometry and Arithmetic Geometry

Abstract

We define a superspace over a ring $R$ as a functor on a subcategory of the category of supercommutative $R$-algebras. As an application the notion of a $p$-adic superspace is introduced and used to give a transparent construction of the Frobenius map on $p$-adic cohomology of a smooth projective variety over the ring of $p$-adic integers.

14 pages, expanded introduction, more details

References in corpus (4)

• Integrality of instanton numbers and p-adic B-model
• Integrality of instanton numbers
• Frobenius transformation, mirror map and instanton numbers
• Arithmetic Spacetime Geometry from String Theory

Cited by in corpus (6)

• Integrality of instanton numbers and p-adic B-model
• Twisted de Rham cohomology, homological definition of the integral and "Physics over a ring"
• Integrality theorems in the theory of topological strings
• Supermanifolds from Feynman graphs
• Integrality of Framing and Geometric Origin of 2-functions
• $p$-adic superspaces and Frobenius